Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 32, 48 i.e. 16 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 32 and 48 is **16**.

GCF(32,48) = 16

*Greatest common factor* or Greatest common divisor (GCD) can be calculated in following way;

- Greatest Common Factor of 32 and 48 by prime factorization method
- Greatest Common Factor of 32 and 48 by matching factors method

**Prime Factorization of 32**

2 | 32 |

2 | 16 |

2 | 8 |

2 | 4 |

2 | 2 |

1 |

Prime factors of 32 are 2. Prime factorization of **32** in exponential form is:

32 = 2^{5}

**Prime Factorization of 48**

2 | 48 |

2 | 24 |

2 | 12 |

2 | 6 |

3 | 3 |

1 |

Prime factors of 48 are 2.Prime factorization of **48** in exponential form is:

48 = 2^{4}×3^{1}

∴ So by taking common prime factors GCF of 32 and 48 is 16

**Factors of 32**

List of positive integer factors of 32 that divides 32 without a remainder.

1,2,4,8,16,32

**Factors of 48**

List of positive integer factors of 48 that divides 48 without a remainder.

1,2,3,4,6,8,12,16,24,48

**Greatest Common Factor**

We found the factors and prime factorization of 32 and 48. The biggest common factor number is the **GCF** number.

So the **greatest common factor 32 and 48** is **16**.

Also check out the Least Common Multiple of 32 and 48

(i) The GCF of 32 and 48 is associative

GCF of 32 and 48 = GCF of 48 and 32

1. What is the GCF of 32 and 48?

Answer: GCF of 32 and 48 is 16.

2. What are the Factors of 32?

Answer: Factors of 32 are 1, 2, 4, 8, 16, 32. There are 6 integers that are factors of 32. The greatest factor of 32 is 32.

3. What are the Factors of 48?

Answer: Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 10 integers that are factors of 48. The greatest factor of 48 is 48.

4. How to Find the GCF of 32 and 48?

Answer:

Greatest Common Factor of 32 and 48 = 16

Step 1: Find the prime factorization of 32

32 = 2 x 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 48

48 = 2 x 2 x 2 x 2 x 3

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 2 x 2 x 2 = 16

Step 4: Therefore, the greatest common factor of 32 and 48 is 16